Bernoulli distribution

In probability theory and statistics, the Bernoulli distribution, named after Swiss scientist James Bernoulli, is a discrete probability distribution, which takes value 1 with success probability p and value 0 with failure probability q=1-p. So if X is a random variable with this distribution, we have:

Related Topics:
Probability theory - Statistics - James Bernoulli - Discrete - Probability distribution

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: Pr(X=1) = 1- Pr(X=0) = p!.

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The probability mass function f of this distribution is

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: f(k;p) = left{egin{matrix} p & mbox {if }k=1, \

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1-p & mbox {if }k=0, \

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0 & mbox {otherwise.}end{matrix} ight.

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The expected value of a Bernoulli random variable X is EX=p, and its variance is

Related Topics:
Expected value - Variance

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: extrm{var}(X)=p(1-p),.

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The Bernoulli distribution is a member of the exponential family.

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